# LABORATORY 2 THE DIFFERENTIAL AMPLIFIER

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1 LABORATORY 2 THE DIFFERENTIAL AMPLIFIER OBJECTIVES 1. To understand how to amplify weak (small) signals in the presence of noise. 1. To understand how a differential amplifier rejects noise and common mode signals. 2. To evaluate the roles of the components of a differential amplifier. 3. To test the operation of a current source in place of an emitter resistor. 4. To simulate the dc conditions of various differential amplifier circuits using MicroCap software. INFORMATION A differential amplifier is a basic building block seen as the first stage of an operational amplifier. Its importance to the success of the op-amp is paramount. A differential amplifier provides two input and two output terminals. The amplifier is powered by split supplies, also the norm for op-amps. Although the op-amp has two input terminals, the input to be amplified is usually connected between one input and circuit ground. The other input is used for feedback and other purposes. This experiment will consider the dc biasing and ac small signal aspects of differential amplifier operation, beginning with the circuit of Figure 1. Icc Rc1 Ic1 Ic2 Rc2 Vcc Vo1 Vo2 Rb1 Q1 Q2 Rb1 Vs1 Ib1 Ie1 Ie2 Ib2 Vs2 Re Iee Figure 1. Basic BJT differential amplifier circuit. Ideally both transistors Q1 and Q2 should have equal parameters, so the Equations (1) and (2) could describe the current values in this circuit. I cc I c1 = I c2 = (1) 2 3-1

2 I ee I e1 = I e2 = (2) 2 A preferred simple circuit of a real differential amplifier is given in Figure 2 and it is using a current source (in the emitters) to DC bias Q1 and Q2. This current source is designed to overcome variations in the transistors parameters and for temperature compensation. The design of a current source is provided below. Vcc Vo1 Ic1 Rc1 Rc2 Vo2 Vs1 Rb1 Q1 Q2 Rb1 Vs2 R1 Vb3 Q3 R2 Iee Re Figure 2. Differential amplifier with a current source. For DC biasing of the differential amplifier shown in Figure 2 the following equations could be used. V cc = I c1 Rc 1 + VCE1 + VCE 3 + I eere + (3) With some approximation the following equation could be used for dc biasing of this circuit: V + b3 = VBE3 + I eere (4) PRE-LABORATORY PREPARATION The lab preparation must be completed before coming to the lab. Show it to your TA for checking and grading (out of 15) at the beginning of the lab and get his/her signature. 1. Select the BJT pair You will be provided with four 2N3904 NPN transistors. You need to select two NPNs that are reasonably matched for the basic differential amplifier, and one NPN for the current source. Use the curve tracer software on the computer in SEB3108 to obtain the 3-2

3 input and output characteristics for each of the transistors. Try to match two 2N3904 transistors to be used as the basic two transistors in the differential pair. A note of warning, do not damage one of the transistors in the differential pair. If you lose one you may have to start all over again! 2. Circuit design Use the circuit of Figure 2 as a model to design a differential amplifier with a current source. Set the DC power supply voltage at ±10 V DC. Include a base resistance R b1 =R b2 =10 kω in each input. Design the circuit such that V CE = 4.5 V for the two transistors in the differential pair. Similarly set V CE = 4.5 V for the current source (transistor Q 3 ). Select I C1 = I C2 =2 ma through each transistor in the differential pair, the constant current source will then have to provide an I CC = I EE = 4 ma. Assume the DC h FE = 175 (h FE =β) (unless you match two NPNs and have a different value), and V BE = 0.7 V. Set the voltage V B3 = -5V, using resistors R 1 = R 2 = 10 kω. Equations (3) and (4) should be of help in determining the R C1 = R C2 and R e component values. Remember the standard values for the resistors that are available in the box in SEB3107 and use only one resistor for each location. You may have somewhat different voltages and currents in the lab. 3. Small signal models of the circuit The DC operating point values for V CE, I C, and I B for each transistor in the circuit were given. Use the small signal model for the transistor and calculate the low frequency (1 khz) voltage gain for the following case: 3.1. From the input of Q1 to the output of Q1 and Q2, with the input of Q2 connected to ground Similarly from the input of Q2 to the output of Q1 and Q2 with the input of Q1 connected to ground. Keep track of the phase angle in each situation. Use this value to compare with the simulation Connect the two inputs together to the same voltage source. Calculate the voltage gain from the input voltage to one or both outputs (Q1 and Q2). Compare your results with the simulation below. (Common mode signals and/or noise) 3.4. Calculate the input impedance at one input with the other input connected to ground. 4. MicroCap simulations Set the circuit in Figure 2 using calculated components values for resistors R C1 = R C2 and R e Determine the DC quiescent values for V CE, V BE and I C for each transistor Use Table 3.1 to compare the experimental data, the calculated values and the results obtained from the simulation With the input signal connected to one input and the second input grounded, determine the frequency response of the voltage gain (magnitude in db and phase) to the collectors of 3-3

4 Q1 and Q2. Use a frequency range from 50 Hz to 1 MHZ. Plot two separate sets of curves and bring them to your lab session. Attention: You must plot the Bode plots, i.e. the ratio of the output voltage over the input voltage, not the output voltage by setting the input voltage equal to 1.0 0! MicroCap simulations tips: To provide a power supply to the circuit use two Battery sources from the MicroCap library. Connect them as Vcc and voltage sources with common ground and set them to 10VDC. To obtain the values of the all the bias currents and voltages on your schematic choose the Probe AC mode from Analysis menu and click on Node Voltages and Currents icons on the toolbar. For a sine wave signal source (used for simulating the Vin), use a 1MHz Sinusoidal Source from the Micro Cap library. Set the AC Amplitude to A= 0.02(V) in the model description area of the signal source. Note that A=0.02V corresponds to a magnitude of V p-p =0.04V. To obtain the gain and phase frequency response plots for this circuit you must run AC ANALYSIS. To get best results for your plots set the AC Analysis Limits as follows: Frequency Range: 1E6,10 which corresponds to a frequency range from 10 Hz to 1MHz Plot parameters: P* X-Expression Y-Expression** X-Range Y-Range Voltage Gain Q1 1 F db(v(3)/v(1)) 1e6,10,1k 30,0,5 Phase Q1 2 F ph(v(3)/v(1)) 1e6,10,1k 200,60,20 Voltage Gain Q2 3 F db(v(5)/v(1)) 1e6,10,1k 30,0,5 Phase Q2 4 F ph(v(5)/v(1)) 1e6,10,1k 10,-90,20 Note: * Set parameter P (plot #) to plot separate diagram for each curve **V(1), V(3) and V(5) are the AC voltages at corresponding node (1) at the input and nodes (3) and (5) at the output of the simulation circuit set up. In your particular case they could have different numeration With the input signal connected to both inputs in parallel, determine the frequency response of the voltage gain (magnitude in db and phase) to the collectors of Q1 and Q2. Use a frequency range from 50 Hz to 1 MHZ. Plot separate sets of curves and bring them to your lab session. To get best results for your plots set the AC Analysis Limits as follows: Frequency Range: 1E6,10 which corresponds to a frequency range from 10 Hz to 1MHz Plot parameters: P* X-Expression Y-Expression** X-Range Y-Range Voltage Gain Q1 1 F db(v(3)/v(1)) 1e6,10,1k 0,-60,10 Phase Q1 2 F ph(v(3)/v(1)) 1e6,10,1k -100,-200,20 Voltage Gain Q2 3 F db(v(5)/v(1)) 1e6,10,1k 0,-60,10 Phase Q2 4 F ph(v(5)/v(1)) 1e6,10,1k -100,-200,20 3-4

5 EQUIPMENT 1. Digital multimeter (Fluke 8010A, BK PRECISION 2831B) 2. Digital oscilloscope Tektronix TDS Function Generator Wavetek FG3B. 4. PROTO-BOARD PB-503 (breadboard). 5. BJT 2N Resistors 10 kω 4. PROCEDURE 1. Connect the differential amplifier shown in Figure 3 using calculated values of R C1 = R C2 and R e. You will obtain better results if you match the two transistors in the differential pair using the curve tracer output characteristics. 2. Use a dual voltage Power Supply and connect its POS terminal as Vcc, NEG terminal as and COM terminal as a common ground. Set the power supply voltage to 10V DC. Measure the DC quiescent point values. Use Table 1 to compare the voltages and currents from your calculations and from the simulation with the experimental data. If your results are significantly different (more than 15%) from your calculated and simulated values, try to find out and eliminate the reason for that discrepancy. Calculation Simulation Experiment Table 1. Q1 Q2 Q3 V CE V BE I C V CE V BE I C V CE V BE I C CH1 CH2 CH1 CH2 PHASE METER OUT Vcc Rc1 Rc2 INPUT FG Vs1 Q1 Vo1 Vo2 Q2 Q3 Re Figure 3. Differential amplifier frequency response measurements. 3-5

6 3. Connect the signal generator (FG) to the Q1 input with the Q2 input connected to ground as it is shown in Figure 3. Increase the input signal to one input (Q1). Determine the maximum output signal the circuit will produce without distortion. Use a frequency of 1 khz. Compare this result with the V CE of the two transistors in the differential pair and with V CC. 4. Set the frequency at 1 khz and determine the input resistance as seen at Q1 with the input of Q2 connected to common ground. 5. With the input signal connected to one input and the second input grounded, determine the frequency response of the voltage gain (magnitude in db and phase) to the collectors of Q1 and Q2. Set the amplitude of the Function Generator (FG) to 50mV. Sweep a frequency range from 50 Hz to 1 MHz and collect all data in Table Connect both Ch1 of the oscilloscope and the Phase meter in parallel to the input signal. Connect both Ch2 of the oscilloscope and the Phase meter in parallel to the output 1 (Q1) signal. Read both instruments and then switch the out measurement terminal to the output 2 (Q2) signal. Change the frequency of the signal generator and repeat the measurements for both outputs. Note which output provides the inverting output and which one the non-inverting output. 7. Calculate the voltage gain A Q1 [db] and A Q2 [db] for both outputs of the differential amplifier, using equation (5). A V out V ( db) = 20log (5) Vin f [Hz] V in [V] V O1 [V] Θ 1 [deg] A Q1 [db] V O2 [V] Θ 2 [deg] A Q2 [db] k 50k 100k 200k 500k 800k 1M Table 2 Frequency response of a differential amplifier. 8. Plot obtained voltage gain and phase data on top of your simulated Bode plots and compare the results. 9. Set the frequency at 1 khz and interchange the two input connections. Determine the voltage gain to the collectors of Q1 and Q2. 3-6

7 10. Connect both inputs to the same voltage source as it is shown in Figure 4 and make the necessary measurements to plot the frequency response of the common mode signal. Increase the input signal up to 6-7 V to be able to measure the output voltage. Vary the frequency from 50 Hz to 1 MHZ and fill all data in a table similar to Table 2. These results will give you an indication how well the differential amplifier rejects the common signal. 11. Plot obtained voltage gain and phase data on top of your simulated Bode plots and compare the results. CH1 CH2 CH1 CH2 PHASE METER OUT Vcc Rc1 Rc2 FG Vs1 INPUT Q1 Vo1 Vo2 Q3 Re Q2 Figure 4. The common mode signal frequency response measurements. REPORT Your Lab report is due one week later. Please submit it to your TA in the beginning of your next lab session. Note: You must copy/print the Signature and Marking Sheet from your manual before coming to the lab session. 3-7

8 SIGNATURE AND MARKING SHEET LAB 2 To complete by TA during the lab session Student Name: TA Name: Student # : Check boxes Task Max. Marks Pre-lab completed 15 Diff. Amplifier DC bias Test completed 15 Diff. Amplifier Test completed 15 Common Mode Test completed 10 Overall Report Preparation 45 TOTAL MARKS 100 Granted Marks TA Signature 3-8

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